How to cook two things at once (that require slightly different temps)

What size are the potatoes? If you are quartering them or cutting into chunks, you can roast the potatoes at 375 degrees; heat the sheet pan while you heat the oven so it's good and hot. Toss the potatoes in oil and salt; throw them onto the hot pan. They'll sizzle! Putting them in 15 minutes before the chicken, as you suggest, is a good idea. They should be done by the time the chicken is roasted; either way, the chicken should rest for a few minutes anyway. If the potatoes aren't done when the chicken is, crank up the heat to 450. I simply cannot imagine though that they will not be done then. In fact, they may well be done sooner. If that's the case, take them out, and then pop them back into the oven to warm up a bit while you're resting the chicken. ;o)